Question

Solve and check:  3 x2 5x 6 x − 1 x 2 = 7 x 3

Answer 1

Answer:

Here, the given expression,

$\frac{3}{x^2+5x+6}+\frac{x-1}{x+2}=\frac{7}{x+3}$,

$\frac{3}{x^2+3x+2x+6}+\frac{x-1}{x+2}=\frac{7}{x+3}$

$\frac{3}{x(x+3)+2(x+3)}+\frac{x-1}{x+2}=\frac{7}{x+3}$

$\frac{3}{(x+3)(x+2)}+\frac{x-1}{x+2}=\frac{7}{x+3}$

$\frac{3+(x-1)(x+3)}{(x+3)(x+2)} = \frac{7}{x+3}$    

$3+(x-1)(x+3)=7(x+2)$

$3+x^2-x+3x-3=7x+14$

$x^2+2x=7x+14$

$x^2+2x-7x-14=0$

$x^2-5x-14=0$

$x^2-7x+2x-14=0$

$x(x-7)+2(x-7)=0$

$(x+2)(x-7)=0$

$\implies x = -2\text{ or } x = 7$

For x = -2,

The right side of the given equation is not defined,

⇒ x = -2 can not be the solution of the given equation.

While for x = 7,

$\frac{3}{7^2+5\times 7+6}+\frac{7-1}{7+2}=\frac{7}{7+3}$,

Hence, the solution of the given equation is,

x = 7.                                                                              

Answer 2

Answer:

x =  7 is a solution.

x = -2 is an extraneous solution .